Well the correct answer from a frequentist perspective is that the probability is either 0 or 1, but there is not enough information to tell which one (actually for question 2 it is possible that the answer is both 0 and 1 (but not anything in between)). So any student who expresses the idea of "I don't know" coherently should get full credit. If we interpret mean or average to be sample rather than population, then the answer is still 0 or 1, but they can compute it. Whether students who give the p-value for the t test should get full, partial, or no credit depends on what you (or other teachers) have stressed. If you have stressed that p-values are definitely not probabilities on the population parameters, then the p-value is not the answer and should not get credit. If the book and lecture were sufficiently vague on the point then they could get some credit.
Either way both questions are clearly poorly worded (from a Bayesian perspective as well).
--
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111
> -----Original Message-----
> From: r-sig-teaching-bounces at r-project.org [mailto:r-sig-teaching-
>bounces at r-project.org] On Behalf Of jose romero
> Sent: Tuesday, July 13, 2010 7:22 AM
> To: r-sig-teaching at r-project.org> Subject: [R-sig-teaching] a statistic-teaching question
>> Dear R-teaching list:
>> I would like to put forward for your consideration an issue which is
> not R related, but statistics-teaching related. Although i know full
> well that this list is intended for discussion of the use of R in
> teaching statistics, I also know that most (if not all) of you out
> there are highly qualified statistics teachers, and as such, I'd like
> to know your opinion on this issue:
>> As a statistics instructor in a open university (distance education),
> part of my job functions consist in grading exams written at the
> central level in my institution and presented by students nationwide.
> Recently, i had to grade an exam of which the first two questions ran
> like this (again, i did not write this exam):
>> 1) The following is a sample of the duration (in minutes) of time
> intervals between queries to a data base:
>> 91 86 71 79 51 51 67 60 79 85
> 68 86 53 45 86 71 82 88 72 67
> 51 51 75 81 76 80 75 76 82 49
> 66 83 84 82 84 76 53 75 70 55
>> What is the probability that the mean time between queries is more than
> 72.5 minutes?
>> 2) For a certain region of the country, the rainfall measurements (in
> mm) during the last 15 years are the following:
>> 580 575 400 750 428 636 825 360
> 850 590 875 735 920 950 550
>> What is the probability that the average rainfall during the last 15
> years is less than 625 mm?
>>> Considering that these are exam questions for an introductory
> statistical inference course (non bayesian), what are your objections,
> as a teacher, to the way these questions are posed? If you had to
> grade exams with such questions, and it is not in your power to cancel
> this exam and re-schedule for another one, how would you grade your
> pupils?
>> Once again, please excuse me for posting these non-R related and very
> absurd questions for your consideration. However, i'd really like to
> know the experts' opinion on this.
>> Thanks in advance,
>> josé romero
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